No IK option under Add Object Constraint
Inverse Kinematics is a way to let the computer calculate bone angles by the position of just one. For example, moving the hand bone around would cause the elbows and shoulders to automatically bend in the correct ways without the animator manually doing it. (I wanted to say this because it seemed like you were confused about what this is).
As such, the Inverse Kinematics constraint cannot be assigned to an entire Armature/Object because it is not a bone.
Instead, with the Armature selected, go into Pose Mode (You can find it under Edit Mode). Inside pose mode, look inside the Properties Editor on the bottom right section of your screen. Find the little blue bone shape with a loop around it. This is the Bone Constraints tab, where individual bones can be constrained. The Inverse Kinematics constraint will also be found here.